A064789 Inverse permutation to A057028.

1, 3, 2, 6, 4, 5, 10, 8, 7, 9, 15, 13, 11, 12, 14, 21, 19, 17, 16, 18, 20, 28, 26, 24, 22, 23, 25, 27, 36, 34, 32, 30, 29, 31, 33, 35, 45, 43, 41, 39, 37, 38, 40, 42, 44, 55, 53, 51, 49, 47, 46, 48, 50, 52, 54, 66, 64, 62, 60, 58, 56, 57, 59, 61, 63, 65, 78, 76, 74, 72, 70, 68

Offset: 1

Author

N. J. A. Sloane, Oct 20 2001

Keywords

• easy
• nonn

Examples

			If viewed as a regular triangle:
  1;
  3,  2;
  6,  4,  5;
 10,  8,  7,  9;
 15, 13, 11, 12, 14;
 21, 19, 17, 16, 18, 20;
 28, 26, 24, 22, 23, 25, 27;
 36, 34, 32, 30, 29, 31, 33, 35;
 45, 43, 41, 39, 37, 38, 40, 42, 44;
 55, 53, 51, 49, 47, 46, 48, 50, 52, 54;
 66, 64, 62, 60, 58, 56, 57, 59, 61, 63, 65;
 78, 76, 74, 72, 70, 68...
		

Links

• Gerhard Ramsebner, As index of Zernike polynomials (animated SVG).
• Index entries for sequences that are permutations of the natural numbers

Programs

PARI

a(n) = my(k=floor((sqrt(8*n)-1)/2)); my(m=2*(n-1)-k*(k+2)); k*(k+1)/2+abs(m)+(m<=0);
for(n=1, 32,  print(n ", ", a(n))) \\ Gerhard Ramsebner, Nov 10 2024

Formula

a(n) = k*(k+1)/2 + abs(m) + [m<=0] where k=floor((sqrt(8*n)-1)/2), m=2*(n-1)-k*(k+2) and [] is the Iverson bracket. - Gerhard Ramsebner, Nov 10 2024

Extensions

More terms from David Wasserman, Aug 14 2002